{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "This routine uses undirected graphs as input and output. That is, if graph[i, j] and graph[j, i] are both zero, then nodes i and j do not have an edge connecting them. If either is nonzero, then the two are connected by the minimum nonzero value of the two." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "This routine loses precision when users input a dense matrix. Small elements < 1E-8 of the dense matrix are rounded to zero. All users should input sparse matrices if possible to avoid it." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If the graph is not connected, this routine returns the minimum spanning forest, i.e. the union of the minimum spanning trees on each connected component." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If multiple valid solutions are possible, output may vary with SciPy and Python version." } ] } ], "title": [], "level": 0, "target": null }, "Warns": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Raises": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Yields": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Methods": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Returns": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "span_tree", "annotation": "csr matrix", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The N x N compressed-sparse representation of the undirected minimum spanning tree over the input (see notes below)." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Return a minimum spanning tree of an undirected graph" } ] } ], "title": [], "level": 0, "target": null }, "Receives": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Warnings": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Attributes": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Parameters": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "csgraph", "annotation": "array_like or sparse array or matrix, 2 dimensions", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The N x N matrix representing an undirected graph over N nodes (see notes below)." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "overwrite", "annotation": "bool, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If true, then parts of the input graph will be overwritten for efficiency. Default is False." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A minimum spanning tree is a graph consisting of the subset of edges which together connect all connected nodes, while minimizing the total sum of weights on the edges. This is computed using the Kruskal algorithm." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "versionadded", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionadded 0.11.0" } ] } ] } ], "title": [], "level": 0, "target": null }, "Other Parameters": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null } }, "_ordered_sections": [ "Summary", "Extended Summary", "Parameters", "Attributes", "Methods", "Returns", "Yields", "Receives", "Other Parameters", "Raises", "Warns", "Warnings", "Notes" ], "item_file": null, "item_line": null, "item_type": "cython_function_or_method", "aliases": [ "scipy.sparse.csgraph.minimum_spanning_tree" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "The following example shows the computation of a minimum spanning tree\nover a simple four-component graph::\n\n input graph minimum spanning tree\n\n (0) (0)\n / \\ /\n 3 8 3\n / \\ /\n (3)---5---(1) (3)---5---(1)\n \\ / /\n 6 2 2\n \\ / /\n (2) (2)\n\nIt is easy to see from inspection that the minimum spanning tree involves\nremoving the edges with weights 8 and 6. In compressed sparse\nrepresentation, the solution looks like this:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy.sparse import csr_array\nfrom scipy.sparse.csgraph import minimum_spanning_tree\nX = csr_array([[0, 8, 0, 3],\n [0, 0, 2, 5],\n [0, 0, 0, 6],\n [0, 0, 0, 0]])\nTcsr = minimum_spanning_tree(X)\nTcsr.toarray().astype(int)\n", "execution_status": "success" } ], "title": [], "level": 0, "target": null }, "see_also": [], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "csgraph", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "overwrite", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "False" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "minimum_spanning_tree" }, "references": null, "qa": "scipy.sparse.csgraph._min_spanning_tree:minimum_spanning_tree", "arbitrary": [], "local_refs": [ "csgraph", "overwrite", "span_tree" ] }